What are the dimensions of a rectangle with an area of 12 square inches if the length is 5 inches less than 3 times the width?

To find the dimensions of the rectangle, we start with the information given: the area of the rectangle is 12 square inches, and the length is 5 inches less than 3 times the width.

Let the width be represented as ( w ). Therefore, the length can be expressed as ( l = 3w - 5 ). The formula for the area of a rectangle is given by the product of its length and width, which leads us to the equation:

[

l \times w = 12

]

Substituting the expression for length into the area equation, we have:

[

(3w - 5) \times w = 12

]

Expanding this gives us:

[

3w^2 - 5w = 12

]

To solve for ( w ), we rearrange the equation as follows:

[

3w^2 - 5w - 12 = 0

]

Next, we can factor this quadratic equation to find the values of ( w ). We look for two numbers that multiply to ( 3 \times -12 = -36 ) and add up to ( -5 ). These numbers are ( -9 \